Symbolic Extensions of Amenable Group Actions and the Comparison Property
In topological dynamics, the Of course, the statement is preceded by the presentation of the concepts of an entropy structure and its superenvelopes, adapted from the case of
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| Hlavní autoři: | , |
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| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Providence, Rhode Island
American Mathematical Society
2023
AMS, American Mathematical Society |
| Vydání: | 1 |
| Edice: | Memoirs of the American Mathematical Society |
| Témata: | |
| ISBN: | 9781470455873, 1470455870 |
| ISSN: | 0065-9266, 1947-6221 |
| On-line přístup: | Získat plný text |
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- Introduction -- Preliminaries on actions of countable amenable groups -- Entropy structure and the easy direction of the main theorem -- Quasitilings and tiling systems -- Quasi-symbolic extensions—the hard direction of the main theorem -- The comparison property -- Encodable tiling systems -- Appendix A
- Cover -- Title page -- Chapter 1. Introduction -- 1.1. Motivation -- 1.2. Subject of the paper -- 1.3. Organization of the paper -- Acknowledgment -- Chapter 2. Preliminaries on actions of countable amenable groups -- 2.1. Group actions, subshifts, symbolic extensions, block codes -- 2.2. An -modification, ( , )-invariance, Følner sequence, amenability -- 2.3. The Choquet simplex of invariant probability measures -- 2.4. The ergodic theorem -- 2.5. Entropy -- 2.6. Zero-dimensional systems -- Chapter 3. Entropy structure and the easy direction of the main theorem -- 3.1. Structures -- 3.2. Superenvelopes -- 3.3. Definition of the entropy structure -- 3.4. Symbolic extensions-the easy direction -- Chapter 4. Quasitilings and tiling systems -- 4.1. Terminology and facts not requiring amenability -- 4.2. Terminology and facts requiring amenability -- 4.3. Tiled entropy -- Chapter 5. Quasi-symbolic extensions-the hard direction of the main theorem -- Chapter 6. The comparison property -- 6.1. Definition of the comparison property -- 6.2. Banach density interpretation of the comparison property -- 6.3. Comparison property of subexponential groups -- Chapter 7. Encodable tiling systems -- 7.1. Encodable systems of quasitilings -- 7.2. Encodability of tiling systems versus the comparison property -- 7.3. Symbolic extensions for actions of selected groups -- Appendix A -- Bibliography -- Back Cover